Do you use a shammy cream?
I just changed my saddle from the Selle Italia w/cutout to a slightly wider Selle Italia Prolink light genuine gel w/out a cutout. After riding it for the first time today, I didn't get saddle sore but my "girl parts" were not entirely happy on the ride. Part of it was from being squashed against that saddle and part of it is that it's not dialed in yet. I'm not trying to be crude or gross but I did learn that I didn't have enough lubrication to prevent the rawness from the friction of the saddle. I put chamois cream on the liner which was sufficient for the other saddle, but I didn't put anything in my "girl parts" if you will. I was quickly reminded after today's ride that if you lube the chamois well and yourself (I find KY lube works well) that it should't make you chaffed or raw. I am very liberal with each because the chamois does absorb some of it. My shorts had a thinner liner and I think that was part of the problem too. Normally I wear a slightly bulkier liner to absorb any friction and it gives me a little more padding down there.
You may want to try using extra "lube" and/or getting different riding shorts before chucking your new saddle. I found that by making a few minor adjustments an uncomfortable ride becomes much more pleasant. Improper saddle position could also be part of your problem. If you're riding too much on the nose, try moving the saddle forward so you butt is more towards the back end and your soft parts will have more support. Also, is your saddle parallel to the floor? If the nose is too low or high it could result in putting more pressure on your soft tissue. To check mine, I placed a leveler on the saddle and adjusted it until the little bubble was exactly in the middle of the tube. Of course, if these things fail and you still have the tearing issues definitely get rid of the saddle because having happy "girl bits" is much more important.